Question

Find the volume of the prism

Answer 1

The volume of a prism is given by its base area multiplied by its height.

The bases are two right triangles. If we project everything on the xy plane, we can see that the vertices of the base triangle is

$A = (0,0),\quad B = (3,0),\quad C = (0,4)$

So, leg AB is 3 units long, and leg AC is 4 units long. This means that the area of the triangle is

$A = \dfrac{\overline{AB}\times\overline{AC}}{2} = \dfrac{3\times 4}{2} = 6$

The height of the prism connects, for example, points $(0,0,0)$ and $(0,0,5)$, so it's 5 units long. So, the volume of the prism is

$V = A \times h = 6 \times 5 = 30$